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Poisson Distribution definitions

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  • Poisson Distribution
    A probability model for counting occurrences over a fixed interval, using the mean rate of occurrence as its key parameter.
  • Binomial Distribution
    A probability model for counting successes in a fixed number of independent trials, each with the same chance of success.
  • Occurrence
    An event or outcome counted within a fixed interval, such as a bird landing or a car passing.
  • Interval
    A fixed span, often of time or space, over which events are counted in a probability model.
  • Lambda
    The mean rate of occurrence in a fixed interval, serving as the main parameter in the Poisson model.
  • Mean
    The expected number of occurrences in a distribution, equal to lambda in the Poisson model.
  • Variance
    A measure of spread in a distribution, equal to lambda for the Poisson model.
  • Standard Deviation
    The square root of variance, indicating typical deviation from the mean in a Poisson context.
  • Probability Formula
    An expression using lambda, x, e, and factorial to calculate the chance of a specific number of occurrences.
  • Factorial
    The product of all positive integers up to a given number, used in probability calculations.
  • Independence
    A condition where the occurrence in one interval does not affect another, required for Poisson modeling.
  • Poisson PDF
    A calculator function for finding the probability of exactly x occurrences in a Poisson setting.
  • Poisson CDF
    A calculator function for finding the probability of up to a certain number of occurrences in a Poisson model.
  • Approximation
    The use of the Poisson model to estimate binomial probabilities when trials are many and success chance is small.
  • Number Line
    A visual tool representing the fixed interval over which occurrences are counted in Poisson problems.